The present invention relates to correcting a measured signal transmitted through a system.
Effective and accurate measuring of high-speed pulses requires careful design of the measuring setups and methods. Increased measurement accuracy of signals with increasing frequencies together with a high degree of automatization is getting more and more difficult to achieve. While reaching ranges of above 1 GHz, signal distortion resulting from each connection, cables, switches or other elements in the transmission path is influencing the pulse performances significantly, for example with respect to pulse rise and/or fall time, ringing, droop, overshoot, or the like. Such kind of distortion is generally tried to be minimized by using (usually more expensive) high-speed cables, high-frequency connectors, switches, etc. and/or by optimizing the measurement set-up to minimize signal connection lengths. Moreover, a certain trade off between measurement accuracy and the degree of measurement automatization is often required.
Another approach for improving measuring signals can be accomplished by determining the distortion of the signal transmission path and recalculating an ideal signal (i.e. without being distorted by the signal transmission path) from the actually measured signal. The techniques for recalculating the ideal signal are well established in the theory of communications. The response of a linear system to a signal can be determined in the time domain by using the principle of convolution, and in the frequency domain by applying the principle of superposition to responses produced by the individual frequency components applied for the frequency domain representation. Multiplication in the frequency domain is equivalent to convolution in the time domain, and vice versa. A detailed break down of the theory, both for time domain and frequency domain analysis, can be readily taken e.g. from the introductory chapter “Signals and Channels” in “Telecommunications engineering”, ISBN 0-412-38190-7, by J. Dunlop.
For the sake of simplicity and since signal recalculations are mainly applied in the frequency domain, the principle of signal recalculation shall be explained in the following mainly with respect to frequency domain analysis. It is clear, however, that signal recalculations in the time domain applying convolution techniques can be applied accordingly.
FIG. 1 illustrates the principle of signal recalculation in the frequency domain. An input signal 10 provided from a signal source 20 is transmitted through a communication channel generally represented herein as a system 30. In general, the system 30 modifies or distorts the waveform of the input signal 10 transmitted through the system 30 to an output signal 40. The amount of distortion produced by the system 30 is thereby determined by the transfer function (i.e. attenuation and phase shift as a function of frequency) of the system 30. The determination of the transfer function will be explained in more detail with respect to FIG. 2. The output signal 40 is measured by a measuring device 50 such as an oscilloscope.
Before recalculating the input signal 10 from the output signal 40 by a recalculation unit 60, a window function W is usually applied to the measured output signal 40 for reducing spectral leakage effects. Typical window functions are Hanning-Window, Blackman Window, or Hamming Window. The recalculation unit 60 then transforms the windowed signal from the time domain into the frequency domain usually by applying a Fast Fourier Transformation (FFT). The transformed signal is then divided by the transfer function T(f) of the system 30, and the result thereof is retransformed from the frequency domain back into the time domain usually by applying an Inverse Fast Fourier Transformation (IFFT). The result of the retransformation represents a recalculated signal 70, which substantially corresponds to the input signal 10. The recalculated signal 70 might be applied to a signal source 80 for generating a physical signal 90 from the recalculated signal 70 or could be applied for analyzing the recalculated signal 70 with respect to its characteristics and properties.
It is clear that the recalculated signal 70 ideally equals the input signal 10 in case that:                the transfer function T(f) applied in the recalculation unit 60 fully equals the transfer function of the system 30,        The transformation and retransformation steps are completely inverse,        the measuring device 50 and the recalculation unit 60 have no transfer function(s) further modulating the signals, and        the window function W has no influence on the signals.        
It is clear that any deviation from the ideal situation as outlined above will adversely affect the signal recalculation process and lead to deviations of the recalculated signal 70 from the input signal 10.
FIG. 2 illustrates the principle for determining a transfer function. A reference signal generator 100 applies a reference signal 110 to the system 30 for which the transfer function T(f) is to be determined. The reference signal 110 transmitted through the system 30 is distorted to a signal response 120 measured by a first measuring device 130. The measured signal response 120 is modulated by a window function (block W) and transformed into the frequency domain (block FFT) as a function O(f). Accordingly, the reference signal 110 is measured by a second measuring device 140, modulated by a window function (block W) and transformed into the frequency domain (block FFT) as a function I(f). The transfer function T(f) of the system 30 is then determined in a calculation unit 150 by dividing the frequency-transformed signal response O(f) by the frequency-transformed reference signal I(f).
It is clear that—dependent on the characteristics of the respective signals—the window functions W applied in FIGS. 1 and 2 can either be the same or different window functions.
Another way for determining the transfer function T(f) would be to measure the response of the system 30 to an applied Dirac pulse.
As noted above, the frequency domain analysis executed by the recalculation unit 60 in FIG. 1 can also be undertaken in the time domain, since the time domain and the frequency domain are linked by the Fourier transform. In that case, the recalculation unit 60 would provide a convolution analysis, however, leading correspondingly to the recalculated signal 70.
When performing the recalculation as outlined for FIG. 1, several difficulties are encountered:                Firstly, sampling oscilloscopes are generally applied as standard measurement instruments for characterizing (digital) signals, e.g. for determining overshoot or ringing of a digital pulse. For achieving highest accuracy on signal performance measurements, it is necessary to set the time base of the oscilloscope to a value that shows only a few signal periods or even less than one signal period on the screen. This allows maximizing the sampling density of the measured signal. On the other hand, for performing the frequency transformation (such as FFT) a significant number of periods of the measured signal should be used for minimizing the effect of the signal windowing on the measurement accuracy.        High sampling resolution and to put a huge number of signal periods into one screen shot for minimizing windowing effects, however, are contravening requirements, and a certain trade off between those requirements has to be made. However, it is apparent that any limitation of the sampling accuracy in the measuring process of FIG. 1 will correspondingly lead to a reduced accuracy of the recalculated signal 70 with respect to the input signal 10. Accordingly, any inaccuracy in the sampling process of FIG. 2 (by the measuring devices 130 and 140) will lead to a reduced accuracy of the transfer function T(f), which again reduces the accuracy of the recalculation process in the recalculation unit 60 of FIG. 1.        Secondly, the transfer function T(f) can only be determined for discrete frequencies and a limited frequency range. That means, that if the time base of the measuring device 50 has to be changed, the transfer function should be determined again. That requires a huge effort for characterizing each measurement path for all different time bases used.        Thirdly, even with highest accuracy for the sampling process and determination of the transfer function, the recalculated signal 70 is still slightly distorted under the influence of the windowing function.        Fourthly, the determination of the transfer function is strongly dependent on the quality of the reference signal generator 100 providing the reference signal 110. Any frequency limitation of the reference source 110 will automatically reduce the accuracy of the determined transfer function.        